A Transformational Approach to Resource Analysis with Typed-Norms

In order to automatically infer the resource consumption of programs, analyzers track how data sizes change along a program s execution. Typically, analyzers measure the sizes of data by applying norms which are mappings from data to natural numbers that represent the sizes of the corresponding data. When norms are defined by taking type information into account, they are named typed-norms. The main contribution of this paper is a transformational approach to resource analysis with typed-norms. The analysis is based on a transformation of the program into an intermediate abstract program in which each variable is abstracted with respect to all considered norms which are valid for its type. We also sketch a simple analysis that can be used to automatically infer the required, useful, typed-norms from programs.This work was funded partially by the EU project FP7-ICT-610582 ENVISAGE: Engineering Virtualized Services (http://www.envisage-project.eu) and by the Spanish projects TIN2008-05624 and TIN2012-38137. Raúl Gutiérrez is also partially supported by a Juan de la Cierva Fellowship from the Spanish MINECO, ref. JCI-2012-13528.Albert Albiol, EM.; Genaim, S.; Gutiérrez Gil, R. (2014). A Transformational Approach to Resource Analysis with Typed-Norms. Lecture Notes in Computer Science. 8901:38-53. https://doi.org/10.1007/978-3-319-14125-1_3S38538901Albert, E., Arenas, P., Genaim, S., Gómez-Zamalloa, M., Puebla, G.: Cost Analysis of Concurrent OO Programs. In: Yang, H. (ed.) APLAS 2011. LNCS, vol. 7078, pp. 238–254. Springer, Heidelberg (2011)Albert, E., Arenas, P., Genaim, S., Puebla, G., Zanardini, D.: Cost Analysis of Java Bytecode. In: De Nicola, R. (ed.) ESOP 2007. LNCS, vol. 4421, pp. 157–172. Springer, Heidelberg (2007)Albert, E., Arenas, P., Genaim, S., Puebla, G., Zanardini, D.: Removing Useless Variables in Cost Analysis of Java Bytecode. In: Proc. of SAC 2008, pp. 368–375. ACM (2008)Alonso, D., Arenas, P., Genaim, S.: Handling Non-linear Operations in the Value Analysis of COSTA. In: Proc. of BYTECODE 2011. ENTCS, vol. 279, pp. 3–17. Elsevier (2011)Bossi, A., Cocco, N., Fabris, M.: Proving Termination of Logic Programs by Exploiting Term Properties. In: Proc. of TAPSOFT 1991. LNCS, vol. 494, pp. 153–180. Springer (1991)Bruynooghe, M., Codish, M., Gallagher, J., Genaim, S., Vanhoof, W.: Termination Analysis of Logic Programs through Combination of Type-Based norms. TOPLAS 29(2), Art. 10 (2007)Claessen, K., Hughes, J.: QuickCheck: A Lightweight Tool for Random Testing of Haskell Programs. In: Proc. of ICFP 2000, pp. 268–279. ACM (2000)Fähndrich, M.: Static Verification for Code Contracts. In: Cousot, R., Martel, M. (eds.) SAS 2010. LNCS, vol. 6337, pp. 2–5. Springer, Heidelberg (2010)Genaim, S., Codish, M., Gallagher, J.P., Lagoon, V.: Combining Norms to Prove Termination. In: Cortesi, A. (ed.) VMCAI 2002. LNCS, vol. 2294, pp. 123–138. Springer, Heidelberg (2002)Johnsen, E.B., Hähnle, R., Schäfer, J., Schlatte, R., Steffen, M.: ABS: A Core Language for Abstract Behavioral Specification. In: Aichernig, B.K., de Boer, F.S., Bonsangue, M.M. (eds.) Formal Methods for Components and Objects. LNCS, vol. 6957, pp. 142–164. Springer, Heidelberg (2011)King, A., Shen, K., Benoy, F.: Lower-bound Time-complexity Analysis of Logic Programs. In: Proc. of ILPS 1997, pp. 261–275. MIT Press (1997)Serrano, A., Lopez-Garcia, P., Bueno, F., Hermenegildo, M.: Sized Type Analysis for Logic Programs. In: Tech. Comms. of ICLP 2013. Cambridge U. Press (2013) (to appear)Spoto, F., Mesnard, F., Payet, É.: A Termination Analyser for Java Bytecode based on Path-Length. TOPLAS 32(3), Art. 8 (2010)Vallée-Rai, R., Hendren, L., Sundaresan, V., Lam, P., Gagnon, E., Co, P.: Soot - a Java Optimization Framework. In: Proc. of CASCON 1999. pp. 125–135. IBM (1999)Vasconcelos, P.: Space Cost Analysis using Sized Types. Ph.D. thesis, School of CS, University of St. Andrews (2008)Vasconcelos, P.B., Hammond, K.: Inferring Cost Equations for Recursive, Polymorphic and Higher-Order Functional Programs. In: Trinder, P., Michaelson, G.J., Peña, R. (eds.) IFL 2003. LNCS, vol. 3145, pp. 86–101. Springer, Heidelberg (2004)Wegbreit, B.: Mechanical Program Analysis. Commun. ACM 18(9), 528–539 (1975

Methods for Proving Non-termination of Programs

The search for reliable and scalable automated methods for finding counterexamples to termination or alternatively proving non-termination is still widely open. The thesis studies the problem of proving non-termination of programs and presents new methods for the same. It also provides a thorough comparison of new methods along with the previous methods. In the first method, we show how the problem of non-termination proving can be reduced to a question of underapproximation search guided by a safety prover. This reduction leads to new non-termination proving implementation strategies based on existing tools for safety proving. Furthermore, our approach leads to easy support for programs with unbounded non-determinism. In the second method, we show how Max-SMT-based invariant generation can be exploited for proving non-termination of programs. The construction of the proof of non-termination is guided by the generation of quasi-invariants - properties such that if they hold at a location during execution once, then they will continue to hold at that location from then onwards. The check that quasi-invariants can indeed be reached is then performed separately. Our technique produces more generic witnesses of non-termination than existing methods. Moreover, it can handle programs with unbounded non-determinism and is more likely to converge than previous approaches. When proving non-termination using known techniques, abstractions that overapproximate the program's transition relation are unsound. In the third method, we introduce live abstractions, a natural class of abstractions that can be combined with the concept of closed recurrence sets to soundly prove non-termination. To demonstrate the practical usefulness of this new approach we show how programs with non-linear, non-deterministic, and heap-based commands can be shown non-terminating using linear overapproximations. All three methods introduced in this thesis have been implemented in different tools. We also provide experimental results which show great performance improvements over existing methods